Composite plates with through-the-length and through-the-width

λ = l

ξ = 1 λ = l/2

Table 4-3: Critical buckling stresses and buckling wavelengths for plate cases 4, 5, 6 and 7.

VICONOPT Case 4 Case 5 Case 6 Case 7

Nxc (Nmm^-1) 182.46 145.00 145.32 145.36

λ = l l l l

4.1.2 Composite plates with through-the-length and through-the-width delaminations

Plates with the same ply properties and plate dimensions as those used in the previous section were then used to explore the effect of length and through-the-width delaminations. Again, the plates were assumed to be simply supported on all four edges and subjected to a longitudinal compressive force as shown in Figure 4-1

x

y z

x

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(a). They were assumed to have a single through-the-length and through-the-width delamination. The effect of introducing this delamination at different depths was studied, at locations of h/16, h/8, h/4, 3h/8 and h/2 below the top surface, i.e. between the 1^st and 2^nd, 2^nd and 3^rd…...8^th and 9^th plies of the laminate. Figure 4-1 (b) illustrates the case where the delamination is at a depth of h/8.

In each case it was found that the upper plate only buckles, at all depths except when the delamination is located half way through the thickness of the plate (h/2). At this depth, both plates buckle at the same time but in opposite directions due to the symmetry of the layup about the mid-plane as shown in Figure 4-2.

(a)

x

y

43 (b)

Figure 4-1 Ply composite plate (a) the boundary conditions of the plate and the external load applied (NL) (b) the plate with a single full width through-the-length delamination at a depth of 2h/16.

Figure 4-2 First natural frequency mode shape of a plate with through-the-length and through-the-width delamination located at the mid thickness.

l

44

Figure 4-3: Critical buckling force intensities for plates with ply orientation for plate cases 1 and 3 and different delamination depths.

Figure 4-3 shows that the relationship between the depth of the delamination and the buckling load for plates with lay-ups according to cases 1 and 3. As well as the increase in buckling load which occurs with increased depth due to the increased stiffness of the locally buckling upper section, it can be seen that the difference in critical buckling force intensities between cases 1 and 3 increases as the delamination moves towards the mid-thickness of the plate. It can be concluded that, when the delaminationis close to the surface the buckling force intensity is actually the buckling load of the thinner laminate portion of the laminate, which is the lowest. However, the rest of the plate is much thicker and capable of carrying much higher load. When the delamination located at the mid thickness (8h/16), the thickness of the two parts of laminate is equal and larger, and so the buckling force intensity is higher than the other cases of delamination depths. In this work, no contact was modelled between the two parts of the laminate.

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Figure 4-4 presents the same relationships for plates with the ply orientations defined for cases 4, 5, 6 and 7. Again it can be seen that the critical buckling load of the delaminated plates increases as the delamination is moved toward the mid-thickness of the plate. The increasing rate at which the critical buckling force intensity changes as the delamination moves deeper is also demonstrated. This is as expected since the flexural stiffness of the locally buckling upper plate is proportional to the cube of its thickness which effectively increases as the delamination moves towards the centre, directly affecting its critical buckling force intensity. Figure 4-4 also demonstrates the significant effect that the ply orientations of the delaminated part have on the value of the critical buckling load. For instance, the plate case 5 [0⁰/45⁰//-45⁰/90/0⁰/45⁰ /-45⁰/90⁰]S has a critical buckling force intensity of 1.35 N/mm when the full width delamination is located at a depth of 2h/16. In this case, the delaminated part consists of the two plies 0⁰ and 45⁰. However, the plate case 6 [90⁰/45⁰//-45⁰/0⁰/90 /45⁰ /-45⁰/0⁰]S has a critical buckling force intensity of 6.80 N/mm when the full width delamination is located at the same depth resulting in the delaminated part consisting of the two plies 90⁰ and 45⁰. The critical buckling force intensity of the delaminated plate case 6 is therefore five times the critical bulking force intensity of the delaminated plate case 5 under the same conditions. This is due to the fact that the proportion of the load carried by the outer two plies is significantly reduced since the 0⁰ ply which attracts a much higher load than the 90⁰ ply is now moved to the lower plate. Noting that the two cases, 5 and 6, are similar in their ply orientations and the stacking sequences of the plies at 45⁰ and -45⁰, they differ only in the stacking sequence of the plies, 0⁰ and 90⁰, being swapped. This can have a significant effect

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when the delaminated region contains only a small number of plies for instance the case here.

In summary, in terms of the critical buckling load of a composite plate, it can be concluded that combining on-axis and off-axis plies enhances the stiffness of the whole plate. The optimum layup sequence depends on which of the in-plane force systems is applied.

Figure 4-4 Critical buckling force intensities for plates with ply orientations for plate cases 4, 5, 6 and 7 and different delamination depths.